CNAME other domain with my subdomain with masking

Hello,
im stuck with a particular issue here. i have posted it here before, but didnt had time to follow up. now im really stuck and need solution badly.

you see i have a ecommerce solution where each of my customer have their own site hosted on my subdomain. eg. site1.mysite.com, site2.mysite.com

now i want to have my customers own domain to CNAME with my sub-domain. eg. www.domain1.com will work as site1.mysite.com, www.domain2.com will work as site2.mysite.com

i tried with cludflare few things,
i added domain.com in cloudflare as CNAME
Name(domain.com) Value (site1.mysite.com)
it works actually, but when i type domain.com on browser, the url change to site1.mysite.com. is it possible to keep the url domain.com in browser something like url masking.

if its possible, please guide me a bit. if not possible in cloudflare, please suggest me how can i achieve that in alternative way.

And I'm not sure how you handle the include snippets/ssl-wildcard.conf; for two different domains, but that is in general tricky within the same server block.

But the main question is actually; do you want to be able to use ecommerce.mysite.com at all or is the only focus actually domain.com?
If you only want domain.com, then simply remove ecommerce.mysite.com and you're done.